How To Learn Math #3


Recently, I began a MOOC (massive open online course) called How to Learn Math – For Teachers and Parents (2).  More than 40,000 people took the last class – mainly teachers, parents and school administrators. 95% of people completing the end of course survey said that they would change their teaching or ways of helping as a result of the course.  The course offers important new research ideas on learning, the brain, and math that can transform students’ experiences with math and is based on the work of and narrated by Jo Boaler.  It’s divided into 8 sessions and each one ends with a prompt to write a one paragraph summary reflection on the ideas.  My plan is to post those reflections here.

The third session is titled, Mistakes and Persistence.  There are 3 ideas that spoke to me here.

Making mistakes is necessary in learning.  The most successful entrepreneurs are often the ones who made the most mistakes.  They often failed but learned from it and moved on.  If this is necessary in the “real” world then it is necessary in school.  Brain research tells us that when we make a mistake a synapse fires.  Then, when we’re aware of the mistake, another synapse fires.  Yes, a synapse fires whether we realize we’ve made a mistake or not.  We’re not sure why it happens, but it does.  We also know that this process is more significant in a growth mindset brain than in a fixed mindset brain.  Students need to struggle with content but they need to feel good about the struggle.  That means we need to change the way we present this material to them and the way we assess it.

The testing culture has inflicted a lot of damage.  When tracking traditional vs PBL (problem based learning) schools and students who achieve at the same level, PBL schools score higher on national exams 3 years later.  Those students also acquire higher skilled, better paying jobs 8 years later.  This is because in those schools students are rewarded for experimentation and not necessarily for correct answers.  They are rewarded for having good ideas, for trying them and making mistakes.  This creates a culture where student struggle and thinking is valued.  In these environments, students persevere.

In the traditional school, assessments are performed under test and time pressure.  These conditions promote an atmosphere of anxiety and fear which blocks working memory in the brain.  Students do not get better or faster under these conditions.  In fact, it’s been shown that students work more quickly when anxiety and fear is taken away.  Math anxiety across the achievement range has been linked to timed fact tests in students’ early school years.  Even answering the first hand up during questioning reinforces the idea that faster means smarter.  Schools, in countries that are successful, don’t test until the end of the year.  In these schools, students aren’t afraid to try something new, of being creative, or of thinking in a different way.  The tasks assigned in traditional schools don’t tend to require deep thought and students are often told what method to use.  We, as teachers, assume that this process is good for students because they won’t struggle as much but in fact, we’re working together with students to empty the interaction out of learning – the didactic contract.  In these classes, students will always ask the teacher for help instead of risk being wrong.

There are things we can do.  Teach math facts differently. – Fluency Without Fear.  Give students time to struggle. – Faster Isn’t Smarter.  Don’t just praise mistakes, talk about why they’re important. – Show this to your students.  Assign work that encourages mistakes.  If they’re not making mistakes, they’re probably not doing work that’s challenging enough.  Mark mistakes on their papers with stars or a picture of a synapse firing to highlight their importance.  Allow students time to work more deeply by clustering expectations or teaching to the big ideas instead of to specific expectations.


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